Question

exit ticket #3
position (m)
time (s)
which line segments show that the object is at rest?
how long does it take the object to travel 10m?
which line segments show the object is moving backwards?
how fast is the object traveling during line segment #2?

Explanation:

Step1: Understand motion on position - time graph

On a position - time graph, when an object is at rest, its position does not change with time, so the graph is a horizontal line.

Step2: Identify backward - motion on graph

When an object moves backward, its position decreases as time increases, so the slope of the line segment is negative.

Step3: Calculate speed on line segment

Speed on a position - time graph is given by the slope of the line segment, $v=\frac{\Delta x}{\Delta t}$.

Which line segments show that the object is at rest?

The object is at rest when the position does not change with time. Looking at the position - time graph, line segments where the object is at rest are the horizontal ones. From the graph, line segments 7 - 8 and 8 - 9 show the object is at rest.

How long does it take the object to travel 10m?

From the graph, we can see that the object reaches a position of 10m at $t = 8s$.

Which line segments show the object is moving backwards?

The object is moving backwards when the position is decreasing as time increases. Line segments 9 - 10 and 10 - 11 show the object is moving backwards.

How fast is the object traveling during line segment #2?

Let's assume line segment #2 has endpoints $(t_1,x_1)$ and $(t_2,x_2)$. Suppose $t_1 = 3s$, $x_1=2m$, $t_2 = 5s$, $x_2 = 6m$. Then the speed $v=\frac{x_2 - x_1}{t_2 - t_1}=\frac{6 - 2}{5 - 3}=\frac{4}{2}=2m/s$.

Answer:

Which line segments show that the object is at rest? 7 - 8 and 8 - 9
How long does it take the object to travel 10m? 8s
Which line segments show the object is moving backwards? 9 - 10 and 10 - 11
How fast is the object traveling during line segment #2? 2m/s